# Shapes in Mathematics

In Maths, we have come across many interesting concepts and topics that play an important role in our studies and real-life. There are different branches that describe these concepts. In the same way, geometry is one of the important branches of Mathematics, that explains the various shapes and sizes we see in our everyday life.

There are various kinds of shapes in geometry based on dimensions such as two-dimensional and three-dimensional.

## Types of Shapes

Shapes are classified based on 2d geometry and 3d geometry

The 2d shapes are:

• Circle (Locus of points at a equidistant from the center)
• Semi-circle (Half of a circle)
• Triangles (A closed polygon with three sides)
• Quadrilaterals (A closed polygon with four sides)
• Pentagon (Five-sided polygon)
• Hexagon (Six-sided polygon)
• Heptagon (Seven-sided polygon)
• Octagon (Eight-sided polygon)
• Nonagon (Nine-sided polygon)
• Decagon (Ten-sided polygon)

The 3d shapes are:

• Sphere (A closed round figure, whose axes are aligned along x-axis, y-axis and z-axis)
• Cube (It has 6 faces, 12 edges and 8 vertices. All the faces are square in shape. All sides are of equal length)
• Cuboid (It also has 6 faces, 12 edges and 8 vertices. All the faces are in rectangular shape.
• Cone (It has one circular base. The sides of the cone narrow smoothly from surface to the top at a single point, called vertex.)
• Cylinder (It has two parallel circular surfaces and lateral sides in between the circular surfaces.

## Triangles

A triangle is a two-dimensional shape that has three sides and three angles. Now based on sides and angles, triangles are classified into six different categories. They are:

• Scalene triangle (All three sides are of different length)
• Isosceles triangle (Any two sides are equal in length)
• Equilateral triangle (All three sides are equal in length)
• Acute angled triangle (All three angles are acute)
• Right angled triangle (Anyone angle is a right angle)
• Obtuse angles triangle (Anyone angle is obtuse)

## Quadrilaterals

A quadrilateral is a closed shape that has four sides and four angles. These quadrilaterals are also categorised into different types:

• Square (All the four sides are equal and all the four angles measures 90 degrees)
• Rectangle (Opposite sides are equal and the angles are at right angle)
• Rhombus (All sides are equal and diagonals bisect at 90 degrees)
• Parallelogram (Opposite sides are equal and parallel)
• Trapezium (One pair of opposite sides are equal)
• Kite (Two pairs of adjacent sides are equal)

### Conclusion

Shapes are nothing but geometrical figures. These figures represent different forms of objects. Shapes in Maths are usually two-dimensional and three-dimensional. The two-dimensional shapes are aligned across x-axis and y-axis. But three-dimensional objects are defined along three axes such as x-axis,y-axis and z-axis.

Geometric shapes are also classified based on their regularity and irregularity. Regular shapes have uniformity and are symmetrical in nature such as circles, squares, etc. Irregular shapes are non-uniform and non-symmetrical such as trapezium.

Some polygons are also classified as convex and concave polygons. The vertices of the convex polygon are outward the center of the polygon. But in the case of concave polygons, any one of the vertices are inward the center.